\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  3.0  &   & + 10.00 x_{2} & +  1.00 x_{3} & -3.00 x_{4} & -4.00 x_{5} & +  7.00 x_{6} & +  4.00 x_{7} & -7.00 x_{8}\\
 x_{10}   &  3.0 & +  3.00 x_{1} & +  1.00 x_{2} & -1.00 x_{3} & -8.00 x_{4} & +  2.00 x_{5} & +  2.00 x_{6} & -7.00 x_{7} &   \\
 x_{11}   &  0.0 & -6.00 x_{1} & -3.00 x_{2} & -10.00 x_{3} & -2.00 x_{4} & -8.00 x_{5} & +  9.00 x_{6} & + 10.00 x_{7} & +  3.00 x_{8}\\
 x_{12}   &  1.0 & -2.00 x_{1} &   & +  1.00 x_{3} & +  5.00 x_{4} & +  9.00 x_{5} & +  3.00 x_{6} &   & -5.00 x_{8}\\
 x_{13}   &  3.0 & -2.00 x_{1} & -9.00 x_{2} & +  5.00 x_{3} & -9.00 x_{4} & +  5.00 x_{5} & +  3.00 x_{6} & + 10.00 x_{7} & -4.00 x_{8}\\
 x_{14}   &  -3.0 & -6.00 x_{1} & -5.00 x_{2} & -3.00 x_{3} & +  5.00 x_{4} & -6.00 x_{5} & +  5.00 x_{6} & +  3.00 x_{7} & +  3.00 x_{8}\\
 x_{15}   &  -3.0 & -5.00 x_{1} & -7.00 x_{2} & -1.00 x_{3} & +  9.00 x_{4} & -5.00 x_{5} & -2.00 x_{6} & -5.00 x_{7} & -8.00 x_{8}\\
 x_{16}   &  -3.0 & +  2.00 x_{1} & +  9.00 x_{2} & +  2.00 x_{3} & -6.00 x_{4} & -1.00 x_{5} & +  2.00 x_{6} & -1.00 x_{7} & + 10.00 x_{8}\\
 x_{17}   &  -3.0 & +  5.00 x_{1} & -8.00 x_{2} & -8.00 x_{3} & -5.00 x_{4} & -3.00 x_{5} & +  6.00 x_{6} & +  4.00 x_{7} & + 10.00 x_{8}\\
\hline
z    &  0.0 & +  4.00 x_{1} & -1.00 x_{2} & -2.00 x_{3} & +  3.00 x_{4} & -1.00 x_{5} & +  5.00 x_{6} & +  4.00 x_{7} & +  1.00 x_{8}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{8}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,17$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0  &   & -3.00 y_{10} & +  6.00 y_{11} & +  2.00 y_{12} & +  2.00 y_{13} & +  6.00 y_{14} & +  5.00 y_{15} & -2.00 y_{16} & -5.00 y_{17}\\
 y_{2}   &  1.0 & -10.00 y_{9} & -1.00 y_{10} & +  3.00 y_{11} &   & +  9.00 y_{13} & +  5.00 y_{14} & +  7.00 y_{15} & -9.00 y_{16} & +  8.00 y_{17}\\
 y_{3}   &  1.0 & -1.00 y_{9} & +  1.00 y_{10} & + 10.00 y_{11} & -1.00 y_{12} & -5.00 y_{13} & +  3.00 y_{14} & +  1.00 y_{15} & -2.00 y_{16} & +  8.00 y_{17}\\
 y_{4}   &  1.0 & +  3.00 y_{9} & +  8.00 y_{10} & +  2.00 y_{11} & -5.00 y_{12} & +  9.00 y_{13} & -5.00 y_{14} & -9.00 y_{15} & +  6.00 y_{16} & +  5.00 y_{17}\\
 y_{5}   &  1.0 & +  4.00 y_{9} & -2.00 y_{10} & +  8.00 y_{11} & -9.00 y_{12} & -5.00 y_{13} & +  6.00 y_{14} & +  5.00 y_{15} & +  1.00 y_{16} & +  3.00 y_{17}\\
 y_{6}   &  1.0 & -7.00 y_{9} & -2.00 y_{10} & -9.00 y_{11} & -3.00 y_{12} & -3.00 y_{13} & -5.00 y_{14} & +  2.00 y_{15} & -2.00 y_{16} & -6.00 y_{17}\\
 y_{7}   &  1.0 & -4.00 y_{9} & +  7.00 y_{10} & -10.00 y_{11} &   & -10.00 y_{13} & -3.00 y_{14} & +  5.00 y_{15} & +  1.00 y_{16} & -4.00 y_{17}\\
 y_{8}   &  1.0 & +  7.00 y_{9} &   & -3.00 y_{11} & +  5.00 y_{12} & +  4.00 y_{13} & -3.00 y_{14} & +  8.00 y_{15} & -10.00 y_{16} & -10.00 y_{17}\\
\hline
z    &  -0 & -3.00 y_{9} & -3.00 y_{10} &   & -1.00 y_{12} & -3.00 y_{13} & +  3.00 y_{14} & +  3.00 y_{15} & +  3.00 y_{16} & +  3.00 y_{17}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 11 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  4.925 & +  0.15 y_{2} & -15.12 y_{14} & -19.02 y_{11} & -12.42 y_{12} & -16.02 y_{9} & -2.97 y_{6} & -1.10 y_{4} & +  1.63 y_{13} & -18.55 y_{17}\\
 y_{10}   &  0.925 & +  0.15 y_{2} & -6.12 y_{14} & -9.03 y_{11} & -3.42 y_{12} & -5.02 y_{9} & -0.97 y_{6} & -0.10 y_{4} & -3.37 y_{13} & -6.55 y_{17}\\
 y_{3}   &  0.825 & +  0.35 y_{2} & +  0.37 y_{14} & +  6.27 y_{11} & -1.33 y_{12} & +  0.27 y_{9} & -0.28 y_{6} & +  0.10 y_{4} & -9.88 y_{13} & +  3.05 y_{17}\\
 y_{8}   &  1.35 & +  1.30 y_{2} & -17.75 y_{14} & -19.55 y_{11} & -0.35 y_{12} & + 10.45 y_{9} & -1.45 y_{6} & -0.20 y_{4} & -10.25 y_{13} & -28.10 y_{17}\\
 y_{5}   &  10.425 & +  0.15 y_{2} & -42.62 y_{14} & -55.53 y_{11} & -41.93 y_{12} & -40.52 y_{9} & -7.48 y_{6} & -2.10 y_{4} & -9.88 y_{13} & -32.55 y_{17}\\
 y_{16}   &  1.525 & -0.05 y_{2} & -7.12 y_{14} & -9.83 y_{11} & -5.02 y_{12} & -7.82 y_{9} & -1.17 y_{6} & -0.30 y_{4} & -0.38 y_{13} & -5.15 y_{17}\\
 y_{7}   &  18.75 & +  1.50 y_{2} & -106.75 y_{14} & -154.75 y_{11} & -63.75 y_{12} & -93.75 y_{9} & -16.25 y_{6} & -3.00 y_{4} & -45.25 y_{13} & -98.50 y_{17}\\
 y_{15}   &  1.95 & +  0.10 y_{2} & -10.75 y_{14} & -14.35 y_{11} & -6.95 y_{12} & -9.35 y_{9} & -1.65 y_{6} & -0.40 y_{4} & -2.25 y_{13} & -8.70 y_{17}\\
\hline
z    &  7.65 & -0.30 y_{2} & -32.25 y_{14} & -45.45 y_{11} & -26.65 y_{12} & -39.45 y_{9} & -5.55 y_{6} & -1.80 y_{4} & -0.75 y_{13} & -18.90 y_{17}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  0.3 & -0.15 x_{1} & -0.15 x_{10} & -0.35 x_{3} & -1.30 x_{8} & -0.15 x_{5} & +  0.05 x_{16} & -1.50 x_{7} & -0.10 x_{15}\\
 x_{14}   &  32.25 & + 15.12 x_{1} & +  6.12 x_{10} & -0.37 x_{3} & + 17.75 x_{8} & + 42.62 x_{5} & +  7.12 x_{16} & + 106.75 x_{7} & + 10.75 x_{15}\\
 x_{11}   &  45.45 & + 19.02 x_{1} & +  9.03 x_{10} & -6.27 x_{3} & + 19.55 x_{8} & + 55.53 x_{5} & +  9.83 x_{16} & + 154.75 x_{7} & + 14.35 x_{15}\\
 x_{12}   &  26.65 & + 12.42 x_{1} & +  3.42 x_{10} & +  1.33 x_{3} & +  0.35 x_{8} & + 41.93 x_{5} & +  5.02 x_{16} & + 63.75 x_{7} & +  6.95 x_{15}\\
 x_{9}   &  39.45 & + 16.02 x_{1} & +  5.02 x_{10} & -0.27 x_{3} & -10.45 x_{8} & + 40.52 x_{5} & +  7.82 x_{16} & + 93.75 x_{7} & +  9.35 x_{15}\\
 x_{6}   &  5.55 & +  2.97 x_{1} & +  0.97 x_{10} & +  0.28 x_{3} & +  1.45 x_{8} & +  7.48 x_{5} & +  1.17 x_{16} & + 16.25 x_{7} & +  1.65 x_{15}\\
 x_{4}   &  1.8 & +  1.10 x_{1} & +  0.10 x_{10} & -0.10 x_{3} & +  0.20 x_{8} & +  2.10 x_{5} & +  0.30 x_{16} & +  3.00 x_{7} & +  0.40 x_{15}\\
 x_{13}   &  0.75 & -1.63 x_{1} & +  3.37 x_{10} & +  9.88 x_{3} & + 10.25 x_{8} & +  9.88 x_{5} & +  0.38 x_{16} & + 45.25 x_{7} & +  2.25 x_{15}\\
 x_{17}   &  18.9 & + 18.55 x_{1} & +  6.55 x_{10} & -3.05 x_{3} & + 28.10 x_{8} & + 32.55 x_{5} & +  5.15 x_{16} & + 98.50 x_{7} & +  8.70 x_{15}\\
\hline
z    &  -7.65 & -4.92 x_{1} & -0.92 x_{10} & -0.83 x_{3} & -1.35 x_{8} & -10.42 x_{5} & -1.52 x_{16} & -18.75 x_{7} & -1.95 x_{15}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  0.3 & -0.15 x_{1} & -0.15 x_{10} & -0.35 x_{3} & -1.30 x_{8} & -0.15 x_{5} & +  0.05 x_{16} & -1.50 x_{7} & -0.10 x_{15}\\
 x_{14}   &  32.25 & + 15.12 x_{1} & +  6.12 x_{10} & -0.37 x_{3} & + 17.75 x_{8} & + 42.62 x_{5} & +  7.12 x_{16} & + 106.75 x_{7} & + 10.75 x_{15}\\
 x_{11}   &  45.45 & + 19.02 x_{1} & +  9.03 x_{10} & -6.27 x_{3} & + 19.55 x_{8} & + 55.53 x_{5} & +  9.83 x_{16} & + 154.75 x_{7} & + 14.35 x_{15}\\
 x_{12}   &  26.65 & + 12.42 x_{1} & +  3.42 x_{10} & +  1.33 x_{3} & +  0.35 x_{8} & + 41.93 x_{5} & +  5.02 x_{16} & + 63.75 x_{7} & +  6.95 x_{15}\\
 x_{9}   &  39.45 & + 16.02 x_{1} & +  5.02 x_{10} & -0.27 x_{3} & -10.45 x_{8} & + 40.52 x_{5} & +  7.82 x_{16} & + 93.75 x_{7} & +  9.35 x_{15}\\
 x_{6}   &  5.55 & +  2.97 x_{1} & +  0.97 x_{10} & +  0.28 x_{3} & +  1.45 x_{8} & +  7.48 x_{5} & +  1.17 x_{16} & + 16.25 x_{7} & +  1.65 x_{15}\\
 x_{4}   &  1.8 & +  1.10 x_{1} & +  0.10 x_{10} & -0.10 x_{3} & +  0.20 x_{8} & +  2.10 x_{5} & +  0.30 x_{16} & +  3.00 x_{7} & +  0.40 x_{15}\\
 x_{13}   &  0.75 & -1.63 x_{1} & +  3.37 x_{10} & +  9.88 x_{3} & + 10.25 x_{8} & +  9.88 x_{5} & +  0.38 x_{16} & + 45.25 x_{7} & +  2.25 x_{15}\\
 x_{17}   &  18.9 & + 18.55 x_{1} & +  6.55 x_{10} & -3.05 x_{3} & + 28.10 x_{8} & + 32.55 x_{5} & +  5.15 x_{16} & + 98.50 x_{7} & +  8.70 x_{15}\\
\hline
z    &  32.85 & + 22.32 x_{1} & +  5.32 x_{10} & -0.57 x_{3} & + 10.15 x_{8} & + 42.82 x_{5} & +  6.72 x_{16} & + 95.75 x_{7} & +  9.55 x_{15}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  0.3 & -0.15 x_{1} & -0.15 x_{10} & -0.35 x_{3} & -1.30 x_{8} & -0.15 x_{5} & +  0.05 x_{16} & -1.50 x_{7} & -0.10 x_{15}\\
 x_{14}   &  32.25 & + 15.12 x_{1} & +  6.12 x_{10} & -0.37 x_{3} & + 17.75 x_{8} & + 42.62 x_{5} & +  7.12 x_{16} & + 106.75 x_{7} & + 10.75 x_{15}\\
 x_{11}   &  45.45 & + 19.02 x_{1} & +  9.03 x_{10} & -6.27 x_{3} & + 19.55 x_{8} & + 55.53 x_{5} & +  9.83 x_{16} & + 154.75 x_{7} & + 14.35 x_{15}\\
 x_{12}   &  26.65 & + 12.42 x_{1} & +  3.42 x_{10} & +  1.33 x_{3} & +  0.35 x_{8} & + 41.93 x_{5} & +  5.02 x_{16} & + 63.75 x_{7} & +  6.95 x_{15}\\
 x_{9}   &  39.45 & + 16.02 x_{1} & +  5.02 x_{10} & -0.27 x_{3} & -10.45 x_{8} & + 40.52 x_{5} & +  7.82 x_{16} & + 93.75 x_{7} & +  9.35 x_{15}\\
 x_{6}   &  5.55 & +  2.97 x_{1} & +  0.97 x_{10} & +  0.28 x_{3} & +  1.45 x_{8} & +  7.48 x_{5} & +  1.17 x_{16} & + 16.25 x_{7} & +  1.65 x_{15}\\
 x_{4}   &  1.8 & +  1.10 x_{1} & +  0.10 x_{10} & -0.10 x_{3} & +  0.20 x_{8} & +  2.10 x_{5} & +  0.30 x_{16} & +  3.00 x_{7} & +  0.40 x_{15}\\
 x_{13}   &  0.75 & -1.63 x_{1} & +  3.37 x_{10} & +  9.88 x_{3} & + 10.25 x_{8} & +  9.88 x_{5} & +  0.38 x_{16} & + 45.25 x_{7} & +  2.25 x_{15}\\
 x_{17}   &  18.9 & + 18.55 x_{1} & +  6.55 x_{10} & -3.05 x_{3} & + 28.10 x_{8} & + 32.55 x_{5} & +  5.15 x_{16} & + 98.50 x_{7} & +  8.70 x_{15}\\
\hline
z    &  32.85 & + 22.32 x_{1} & +  5.32 x_{10} & -0.57 x_{3} & + 10.15 x_{8} & + 42.82 x_{5} & +  6.72 x_{16} & + 95.75 x_{7} & +  9.55 x_{15}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{13} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  0.230769230769 & +  0.09 x_{13} & -0.46 x_{10} & -1.26 x_{3} & -2.25 x_{8} & -1.06 x_{5} & +  0.02 x_{16} & -5.68 x_{7} & -0.31 x_{15}\\
 x_{14}   &  39.2307692308 & -9.31 x_{13} & + 37.54 x_{10} & + 91.54 x_{3} & + 113.15 x_{8} & + 134.54 x_{5} & + 10.62 x_{16} & + 527.92 x_{7} & + 31.69 x_{15}\\
 x_{11}   &  54.2307692308 & -11.71 x_{13} & + 48.54 x_{10} & + 109.34 x_{3} & + 139.55 x_{8} & + 171.14 x_{5} & + 14.22 x_{16} & + 684.52 x_{7} & + 40.69 x_{15}\\
 x_{12}   &  32.3846153846 & -7.65 x_{13} & + 29.23 x_{10} & + 76.83 x_{3} & + 78.72 x_{8} & + 117.43 x_{5} & +  7.89 x_{16} & + 409.74 x_{7} & + 24.15 x_{15}\\
 x_{9}   &  46.8461538462 & -9.86 x_{13} & + 38.31 x_{10} & + 97.11 x_{3} & + 90.63 x_{8} & + 137.91 x_{5} & + 11.52 x_{16} & + 539.98 x_{7} & + 31.54 x_{15}\\
 x_{6}   &  6.92307692308 & -1.83 x_{13} & +  7.15 x_{10} & + 18.35 x_{3} & + 20.22 x_{8} & + 25.55 x_{5} & +  1.86 x_{16} & + 99.09 x_{7} & +  5.77 x_{15}\\
 x_{4}   &  2.30769230769 & -0.68 x_{13} & +  2.38 x_{10} & +  6.58 x_{3} & +  7.14 x_{8} & +  8.78 x_{5} & +  0.55 x_{16} & + 33.63 x_{7} & +  1.92 x_{15}\\
 x_{1}   &  0.461538461538 & -0.62 x_{13} & +  2.08 x_{10} & +  6.08 x_{3} & +  6.31 x_{8} & +  6.08 x_{5} & +  0.23 x_{16} & + 27.85 x_{7} & +  1.38 x_{15}\\
 x_{17}   &  27.4615384615 & -11.42 x_{13} & + 45.08 x_{10} & + 109.68 x_{3} & + 145.11 x_{8} & + 145.28 x_{5} & +  9.43 x_{16} & + 615.05 x_{7} & + 34.38 x_{15}\\
\hline
z    &  43.1538461538 & -13.74 x_{13} & + 51.69 x_{10} & + 135.09 x_{3} & + 150.97 x_{8} & + 178.49 x_{5} & + 11.88 x_{16} & + 717.42 x_{7} & + 40.46 x_{15}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  0.182926829268 & +  0.07 x_{13} & -0.37 x_{10} & -0.79 x_{2} & -1.78 x_{8} & -0.84 x_{5} & +  0.01 x_{16} & -4.50 x_{7} & -0.24 x_{15}\\
 x_{14}   &  55.9756097561 & -2.61 x_{13} & +  4.05 x_{10} & -72.56 x_{2} & -49.83 x_{8} & + 57.51 x_{5} & + 11.73 x_{16} & + 116.00 x_{7} & +  9.37 x_{15}\\
 x_{11}   &  74.2317073171 & -3.71 x_{13} & +  8.54 x_{10} & -86.67 x_{2} & -55.12 x_{8} & + 79.13 x_{5} & + 15.55 x_{16} & + 192.50 x_{7} & + 14.02 x_{15}\\
 x_{12}   &  46.4390243902 & -2.02 x_{13} & +  1.12 x_{10} & -60.90 x_{2} & -58.07 x_{8} & + 52.78 x_{5} & +  8.83 x_{16} & + 64.00 x_{7} & +  5.41 x_{15}\\
 x_{9}   &  64.6097560976 & -2.76 x_{13} & +  2.78 x_{10} & -76.98 x_{2} & -82.27 x_{8} & + 56.20 x_{5} & + 12.71 x_{16} & + 103.00 x_{7} & +  7.85 x_{15}\\
 x_{6}   &  10.2804878049 & -0.49 x_{13} & +  0.44 x_{10} & -14.55 x_{2} & -12.46 x_{8} & + 10.11 x_{5} & +  2.09 x_{16} & + 16.50 x_{7} & +  1.29 x_{15}\\
 x_{4}   &  3.51219512195 & -0.20 x_{13} & -0.02 x_{10} & -5.22 x_{2} & -4.59 x_{8} & +  3.24 x_{5} & +  0.63 x_{16} & +  4.00 x_{7} & +  0.32 x_{15}\\
 x_{1}   &  1.57317073171 & -0.17 x_{13} & -0.15 x_{10} & -4.82 x_{2} & -4.51 x_{8} & +  0.96 x_{5} & +  0.30 x_{16} & +  0.50 x_{7} & -0.10 x_{15}\\
 x_{17}   &  47.5243902439 & -3.39 x_{13} & +  4.95 x_{10} & -86.94 x_{2} & -50.17 x_{8} & + 52.99 x_{5} & + 10.77 x_{16} & + 121.50 x_{7} & +  7.63 x_{15}\\
\hline
z    &  67.8658536585 & -3.85 x_{13} & +  2.27 x_{10} & -107.09 x_{2} & -89.56 x_{8} & + 64.82 x_{5} & + 13.52 x_{16} & + 109.50 x_{7} & +  7.51 x_{15}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{5}   &  0.217391304348 & +  0.09 x_{13} & -0.43 x_{10} & -0.94 x_{2} & -2.12 x_{8} & -1.19 x_{3} & +  0.01 x_{16} & -5.35 x_{7} & -0.29 x_{15}\\
 x_{14}   &  68.4782608696 & +  2.39 x_{13} & -20.96 x_{10} & -126.74 x_{2} & -171.52 x_{8} & -68.35 x_{3} & + 12.57 x_{16} & -191.57 x_{7} & -7.30 x_{15}\\
 x_{11}   &  91.4347826087 & +  3.17 x_{13} & -25.87 x_{10} & -161.22 x_{2} & -222.57 x_{8} & -94.04 x_{3} & + 16.70 x_{16} & -230.70 x_{7} & -8.91 x_{15}\\
 x_{12}   &  57.9130434783 & +  2.57 x_{13} & -21.83 x_{10} & -110.62 x_{2} & -169.75 x_{8} & -62.72 x_{3} & +  9.59 x_{16} & -218.26 x_{7} & -9.88 x_{15}\\
 x_{9}   &  76.8260869565 & +  2.13 x_{13} & -21.65 x_{10} & -129.91 x_{2} & -201.17 x_{8} & -66.78 x_{3} & + 13.52 x_{16} & -197.52 x_{7} & -8.43 x_{15}\\
 x_{6}   &  12.4782608696 & +  0.39 x_{13} & -3.96 x_{10} & -24.07 x_{2} & -33.86 x_{8} & -12.01 x_{3} & +  2.23 x_{16} & -37.57 x_{7} & -1.64 x_{15}\\
 x_{4}   &  4.21739130435 & +  0.09 x_{13} & -1.43 x_{10} & -8.28 x_{2} & -11.45 x_{8} & -3.86 x_{3} & +  0.68 x_{16} & -13.35 x_{7} & -0.62 x_{15}\\
 x_{1}   &  1.78260869565 & -0.09 x_{13} & -0.57 x_{10} & -5.72 x_{2} & -6.55 x_{8} & -1.14 x_{3} & +  0.32 x_{16} & -4.65 x_{7} & -0.38 x_{15}\\
 x_{17}   &  59.0434782609 & +  1.22 x_{13} & -18.09 x_{10} & -136.86 x_{2} & -162.29 x_{8} & -62.97 x_{3} & + 11.54 x_{16} & -161.87 x_{7} & -7.72 x_{15}\\
\hline
z    &  81.9565217391 & +  1.78 x_{13} & -25.91 x_{10} & -168.14 x_{2} & -226.71 x_{8} & -77.03 x_{3} & + 14.46 x_{16} & -237.13 x_{7} & -11.28 x_{15}\\
\end{array}\]


 $ x_{13} $ enters and $ x_{1} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{5}   &  2.0 & -1.00 x_{1} & -1.00 x_{10} & -6.67 x_{2} & -8.67 x_{8} & -2.33 x_{3} & +  0.33 x_{16} & -10.00 x_{7} & -0.67 x_{15}\\
 x_{14}   &  117.5 & -27.50 x_{1} & -36.50 x_{10} & -284.17 x_{2} & -351.67 x_{8} & -99.83 x_{3} & + 21.33 x_{16} & -319.50 x_{7} & -17.67 x_{15}\\
 x_{11}   &  156.5 & -36.50 x_{1} & -46.50 x_{10} & -370.17 x_{2} & -461.67 x_{8} & -135.83 x_{3} & + 28.33 x_{16} & -400.50 x_{7} & -22.67 x_{15}\\
 x_{12}   &  110.5 & -29.50 x_{1} & -38.50 x_{10} & -279.50 x_{2} & -363.00 x_{8} & -96.50 x_{3} & + 19.00 x_{16} & -355.50 x_{7} & -21.00 x_{15}\\
 x_{9}   &  120.5 & -24.50 x_{1} & -35.50 x_{10} & -270.17 x_{2} & -361.67 x_{8} & -94.83 x_{3} & + 21.33 x_{16} & -311.50 x_{7} & -17.67 x_{15}\\
 x_{6}   &  20.5 & -4.50 x_{1} & -6.50 x_{10} & -49.83 x_{2} & -63.33 x_{8} & -17.17 x_{3} & +  3.67 x_{16} & -58.50 x_{7} & -3.33 x_{15}\\
 x_{4}   &  6.0 & -1.00 x_{1} & -2.00 x_{10} & -14.00 x_{2} & -18.00 x_{8} & -5.00 x_{3} & +  1.00 x_{16} & -18.00 x_{7} & -1.00 x_{15}\\
 x_{13}   &  20.5 & -11.50 x_{1} & -6.50 x_{10} & -65.83 x_{2} & -75.33 x_{8} & -13.17 x_{3} & +  3.67 x_{16} & -53.50 x_{7} & -4.33 x_{15}\\
 x_{17}   &  84.0 & -14.00 x_{1} & -26.00 x_{10} & -217.00 x_{2} & -254.00 x_{8} & -79.00 x_{3} & + 16.00 x_{16} & -227.00 x_{7} & -13.00 x_{15}\\
\hline
z    &  118.5 & -20.50 x_{1} & -37.50 x_{10} & -285.50 x_{2} & -361.00 x_{8} & -100.50 x_{3} & + 21.00 x_{16} & -332.50 x_{7} & -19.00 x_{15}\\
\end{array}\]


 $ x_{16} $ enters and Unbounded Dictionary!


 $ x_{16} $ enters and Unbounded Dictionary!
\end{document}
